Transcript Neutron stars and black holes

Neutron Stars and Black Holes
In the center of the Crab
Nebula there is a neutron
star that pulses every 33
millisec.
J. Bell Burnell
A. Hewish
Pulsars were discovered
serendipitously in 1967
when Jocelyn Bell found
unexplained “noise” in
radio signals from a
particular place in the
sky. Her thesis advisor
eventually won a Nobel
Prize for the explanation.
But first, let us consider how small a compact object might
be. In chapter 4 we find an expression for the escape
speed (Vesc) from an object of mass M:
(Vesc)2 = 2 G M / r
A very small object can have a very large escape speed.
The maximum possible value of the escape speed would
be the fastest speed anything can travel, namely the speed
of light. In other words, what if
c2 = 2 G M / r
?
Rearranging the previous equation, we have
r = 2 G M / c2
With G = 6.67 X 10-11 in MKS units,
Msun = 2.0 X 1030 kg, and
c = 3.0 X 108 m/sec, it follows that
r = 3.0 km.
This would be the radius of a black hole of one
solar mass. If the Earth were squeezed to a radius
of 0.9 cm, it would have an escape speed equal to
the speed of light and would be a black hole.
The radius of a black hole scales linearly with the mass.
Since a 1 solar mass black hole has a radius of 3 km
a 2 solar mass black hole has a radius of 2 X 3 = 6 km
a 10 solar mass black hole has a radius of 10 X 3 = 30 km
a 3 million solar mass black hole has a radius of 3 million
X 3 = 9 million km, or about 13 times the size of our Sun.
(There is strong evidence that the center of our Galaxy
contains a 3 million solar mass black hole. )
OK, back to pulsars. A pulsar is a remnant of the
explosion of a star more massive than 8 solar masses.
Recall that a Type II supernova is the explosion of a
single, massive star. Type Ib and Ic supernovae are
also explosions of single, massive stars, but stars which
have lost their outer envelopes of hydrogen or hydrogen
and helium.
A pulsar does not pulse like a Cepheid variable star.
Rather, it beams out its energy in two opposite
directions, and if one of these beams intersects the
Earth, we see a pulse of radiation.
If the beam of radiation
does NOT intersect the
Earth, then we would
see almost nothing.
Though neutron stars
are very hot, so give
off a lot of radiation
per square meter, they
are very small, so have
very little surface area,
and hence not much
luminosity. The jets
are actually brighter.
The time in between pulses of a pulsar can be determined
with incredible accuracy. They slow down as time goes
on, but occasionally they experience a glitch and speed
up every so slightly before resuming the process of
slowing down.
There are two theories that attempt to explain these
glitches: 1) “starquakes” on the surface of the neutron
star; and 2) vortices in the frictionless interior of the
neutron star transferring angular momentum to the
crust. Both of these theories might be right.
Glitches in
the spin down
of the Vela
pulsar.
A typical pulsar
radius ~ 10 km
mass ~ 1.4 to 3.0 solar masses
temperature ~ 1 million degrees K
(so it gives off X-rays, with
max ~ 3 nm)
Let's compare the total luminosity of a neutron star with
that of the Sun.
LNS = 4  (RNS)2  (TNS)4
Lsun = 4 Rsun)2 (Tsun)4
So
(LNS / Lsun) = (RNS / Rsun)2 (TNS / Tsun)4
With RNS = 10 km, Rsun = 6.96 X 105 km, TNS = one
million degrees K, and Tsun = 5800 K, the total luminosity
of the neutron star is 18 percent that of the Sun. But most
of that light is X-ray light. In the optical, neutron stars might
be 21st magnitude or fainter.
The energy of the supernova explosion that gives
rise to a neutron star/pulsar might be slightly asymmetric.
As a result it can impart a velocity of a couple hundred
km/sec to the neutron star.
PSR 1913+16 is a pair of pulsars that orbit each other
with a period of 7.75 hours. Joseph Taylor and Russell
Hulse were able to show that the orbital period of this
binary pair was getting shorter. This is because the
system is radiating gravitational waves. For this work
Hulse and Taylor were awarded the 1993 Nobel Prize
in physics.
Taylor
Hulse
When the two
neutron stars
eventually come
together, they
can cause another
supernova
explosion!
The pulsar PSR
1257+12 is known
to have three planets.
Two of the planets
have masses of 4.3
and 3.9 Earth masses.
They were discovered
from variations in the
pulsar's period. These
planets did not survive
the SN explosion.
They are remains of
a stellar companion
destroyed by the SN.
Black Holes
Cygnus X-1 is a binary
consisting of a supergiant
B0 star and a compact object.
Wind from the B0 star
flows into the hot accretion
disk of the compact object,
giving rise to X-rays.
If the remnant of a Type II, Ib, or Ic supernova has a mass
greater than 3 solar masses, it is a black hole, not a neutron
star.
How can we tell
the difference between
a neutron star and a
BH acquiring mass
from a companion?
The neutron star
exhibits bursts of
X-rays. Matter that
falls into the BH from
the accretion disk
just disappears.
The central 2 pc
of our Galaxy
contains a rotating
ring of material
around a central
engine. There is
also a very concentrated
star cluster. In the
very center is a
compact object which
causes the stars moving
nearby to acquire
velocities as high as
1400 km/sec
The mass of the
central black hole
is between 2.6 and
3.7 million solar
masses.
Some other galaxies
have black holes
of more than one
billion solar masses
in their cores!
The following little movie shows the paths and
orbits of some stars near the black hole in the
center of our Galaxy.
Courtesy Andrea Ghez, UCLA
The density of black holes
The mass of the proton is 1.67 X 10-24 g, and its radius
is about 0.877 X 10-13 cm (according to the Wikipedia).
The volume of the proton is 4/3  r3 = 2.82 X 10-39 cm3.
The density = mass/volume = 5.9 X 1014 g/cm3.
The Sun’s mass is 2 X 1030 kg = 2 X 1033 g. A one solar
mass black hole has radius r ~ 3 km = 3 X 105 cm. The
average density within the Schwarzschild radius is then
1.8 X 1016 g/cm3. This is 31 times the density of the proton.
So – stellar mass black holes are really dense!
Since the Schwarzschild radius of a black hole is
rSch = 2 GM / c2, the radius of a black hole is proportional to its mass. A one billion solar mass black hole
will have a radius of 3 X 109 km. Since one Astronomical Unit ~ 1.5 X 108 km, it follows that a one
billion solar mass black hole has a radius of about
20 AU, or the size of the orbit of Uranus.
Since the radius of a black hole is proportional to its mass,
and the volume of a sphere is proportional to the cube
of the radius, it follows that the average density within
the Schwarzschild radius is proportional to 1/mass2.
Thus, the mean density of a one billion solar mass
black hole is (1/109)2 lower than a one solar mass
black hole, or (1.8 X 1016) / 1018 ~ 0.018 g/cm3.
A one billion solar mass black hole has a density
at least as small as 2 percent that of water!
So – supermassive black holes are NOT superdense!
Even weirder…say the universe has a mean density
of 6 hydrogen atoms per cubic meter. Neglecting
any effect of “dark energy,” in that case the universe
would keep expanding, but more and more slowly,
until it reached some maximum size. And if the
mean density of the universe were ever so slightly
greater than this, the universe would eventually start
to contract, leading to the Big Crunch (the reverse of
the Big Bang).
If we live in a critical density universe, then the sum of
all the gravitational bending on a laser beam sent out
by us in some direction would cause it eventually to
come around from the other direction.
Another way of looking at that would be that a light beam
is “bound” in a critical density universe. It can’t “get out”.
If even light can’t escape from some object, isn’t that
the definition of a black hole?
If we live in a very low density, but critical-density,
universe, another way of looking at that is: we live inside
a black hole!
The unusual object SS 433
has two precessing jets which
produce pairs of spectral
lines like a spectroscopic
binary but with velocities of
¼ of the speed of light!
Some interacting
systems produce
powerful bursts
of gamma rays.
Many of these
objects are at
distances of
billions of lightyears, so the light
reaching us comes
from explosions
that occurred
billions of years
ago.